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Some Quicker Approximations and Inequalities of the Wallis Ratio by Continued Fraction

Research paper by Xinyu Liu, Dawei Lu; Lixin Song

Indexed on: 23 Sep '16Published on: 01 Nov '16Published in: Results in Mathematics



Abstract

Abstract In this paper, we present a new formula for approximating the Wallis ratio. This new formula is very fast in comparison with other classical or recently discovered asymptotic series. Next, inequalities related to this new formula and asymptotic series are established. Finally, for demonstrating the superiority of our new series, some numerical computations are provided.AbstractIn this paper, we present a new formula for approximating the Wallis ratio. This new formula is very fast in comparison with other classical or recently discovered asymptotic series. Next, inequalities related to this new formula and asymptotic series are established. Finally, for demonstrating the superiority of our new series, some numerical computations are provided.